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State hoops

  • Rajab Ali Borzooei EMAIL logo , Mona Aaly Kologani EMAIL logo and Omid Zahiri EMAIL logo
Published/Copyright: February 28, 2017
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 67 Issue 1

Abstract

In this paper, we define the notions of a state ⊔-hoop and a state-morphism ⊔-hoop extending the language of hoop by adding a unary operator and investigate some properties of them. Also, we extend state ⊔-hoop to state hoop and study the relation between state hoops and state BL-algebras, MV-algebras and BCK-algebras.

MSC 2010: Primary 03G25; 06D99
Keywords: Hoop algebra; state ⊔-hoop; state hoop; state-morphism

(Communicated by Sylvia Pulmannová)

Acknowledgement

The authors wish to express their appreciation for several excellent suggestions for improvements in this paper made by the editor and referees.

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Received: 2013-12-09
Accepted: 2015-03-30
Published Online: 2017-02-28
Published in Print: 2017-03-01

© 2017 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. State hoops
  2. On derivations of partially ordered sets
  3. Interior and closure operators on commutative basic algebras
  4. When is the cayley graph of a semigroup isomorphic to the cayley graph of a group
  5. Sequences of cantor type and their expressibility
  6. δ-Fibonacci and δ-lucas numbers, δ-fibonacci and δ-lucas polynomials
  7. Law of inertia for the factorization of cubic polynomials – the case of primes 2 and 3
  8. Closed hereditary coreflective subcategories in epireflective subcategories of Top
  9. Method of upper and lower solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments
  10. Difference of two strong Światkowski lower semicontinuous functions
  11. Fejér-type inequalities (II)
  12. Representation of maxitive measures: An overview
  13. On a conjecture of Y. H. Cao and X. B. Zhang
  14. On the generalized orthogonal stability of the pexiderized quadratic functional equations in modular spaces
  15. Almost everywhere convergence of some subsequences of Fejér means for integrable functions on some unbounded Vilenkin groups
  16. Homological properties of banach modules over abstract segal algebras
  17. Variable Hajłasz-Sobolev spaces on compact metric spaces
  18. Commuting pairs of self-adjoint elements in C*-algebras
  19. Additivity of maps preserving products AP ± PA* on C*-algebras
  20. A note on derived connections from semi-symmetric metric connections
  21. Lindelöf P-spaces need not be Sokolov
  22. Strong convergence properties for arrays of rowwise negatively orthant dependent random variables
  23. Least absolute deviations problem for the Michaelis-Menten function
  24. Congruence pairs of principal p-algebras
https://doi.org/10.1515/ms-2016-0242
Keywords for this article
Hoop algebra; state ⊔-hoop; state hoop; state-morphism

Articles in the same Issue

  1. State hoops
  2. On derivations of partially ordered sets
  3. Interior and closure operators on commutative basic algebras
  4. When is the cayley graph of a semigroup isomorphic to the cayley graph of a group
  5. Sequences of cantor type and their expressibility
  6. δ-Fibonacci and δ-lucas numbers, δ-fibonacci and δ-lucas polynomials
  7. Law of inertia for the factorization of cubic polynomials – the case of primes 2 and 3
  8. Closed hereditary coreflective subcategories in epireflective subcategories of Top
  9. Method of upper and lower solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments
  10. Difference of two strong Światkowski lower semicontinuous functions
  11. Fejér-type inequalities (II)
  12. Representation of maxitive measures: An overview
  13. On a conjecture of Y. H. Cao and X. B. Zhang
  14. On the generalized orthogonal stability of the pexiderized quadratic functional equations in modular spaces
  15. Almost everywhere convergence of some subsequences of Fejér means for integrable functions on some unbounded Vilenkin groups
  16. Homological properties of banach modules over abstract segal algebras
  17. Variable Hajłasz-Sobolev spaces on compact metric spaces
  18. Commuting pairs of self-adjoint elements in C*-algebras
  19. Additivity of maps preserving products AP ± PA* on C*-algebras
  20. A note on derived connections from semi-symmetric metric connections
  21. Lindelöf P-spaces need not be Sokolov
  22. Strong convergence properties for arrays of rowwise negatively orthant dependent random variables
  23. Least absolute deviations problem for the Michaelis-Menten function
  24. Congruence pairs of principal p-algebras
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